Why does sedimentation continue to fill the basins, albeit typically rather slowly, during the post-rift phase?

Subsidence is so slow that there seems to have been no depression of the upper surface of the lithosphere, so depositional environments are mostly the

same as those in surrounding areas; the succession is just thicker. These

successions are also more complete, however—there are fewer and smaller

diastems—so at times the basin must have remained under water while surrounding areas were emergent. (A diastem is a brief interruption in

sedimentation, with little or no erosion before sedimentation resumes.)

Size, shape: rounded, equidimensional, hundreds of kilometers across

Sediment fill: shallow-water cratonal sediments (carbonates, shales, sandstones),

thicker and more complete than in adjacent areas of the craton but still

relatively thin, hundreds of meters.

Hopefully that helps!